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Related Concept Videos

Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Quantifying and Rejecting Outliers: The Grubbs Test01:02

Quantifying and Rejecting Outliers: The Grubbs Test

Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This number is...
Decision Making: Traditional Method01:14

Decision Making: Traditional Method

The process of hypothesis testing based on the traditional method includes calculating the critical value, testing the value of the test statistic using the sample data, and interpreting these values.
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a...
Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...

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Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
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Regularization Parameter Selections via Generalized Information Criterion.

Yiyun Zhang1, Runze Li, Chih-Ling Tsai

  • 1Yiyun Zhang is a Senior Statistician, Novartis Pharmaceuticals Corporation ( yiyun.zhang@novartis.com ). Runze Li is the correspondence author and Professor, Department of Statistics and The Methodology Center, The Pennsylvania State University, University Park, PA 16802-2111 ( rli@stat.psu.edu ). Chih-Ling Tsai is Robert W. Glock Chair professor, Graduate School of Management, University of California, Davis, CA, 95616-8609 ( cltsai@ucdavis.edu ).

Journal of the American Statistical Association
|August 3, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces the generalized information criterion (GIC) for selecting regularization parameters in nonconcave penalized likelihood methods. The Bayesian information criterion (BIC)-type selector consistently identifies the true model, unlike the Akaike information criterion (AIC)-type selector which may overfit.

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A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment
12:18

A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment

Published on: January 11, 2020

Area of Science:

  • Statistics
  • Machine Learning
  • Econometrics

Background:

  • Nonconcave penalized likelihood methods are crucial for variable selection and shrinkage estimation.
  • Effective regularization parameter selection is vital for controlling model complexity in these methods.
  • Existing criteria like AIC and BIC have limitations in this context.

Purpose of the Study:

  • To propose the generalized information criterion (GIC) for selecting regularization parameters in nonconcave penalized likelihood approaches.
  • To establish a link between classical variable selection criteria and regularization parameter selection.
  • To evaluate the performance of BIC-type and AIC-type selectors.

Main Methods:

  • Application of nonconcave penalized likelihood.
  • Development and application of the generalized information criterion (GIC).
  • Theoretical analysis of BIC-type and AIC-type selectors, including oracle property and asymptotic efficiency.

Main Results:

  • The BIC-type selector consistently identifies the true model and exhibits the oracle property.
  • The AIC-type selector demonstrates asymptotic loss efficiency but tends to overfit.
  • Simulation results validate the theoretical findings.

Conclusions:

  • The GIC provides a robust framework for regularization parameter selection in nonconcave penalized likelihood.
  • The BIC-type selector is preferred for consistent model identification and oracle property.
  • The AIC-type selector offers asymptotic efficiency but carries a risk of overfitting.